Let O be an interior points of `triangleABC` such that `vec(OA)+vec(OB)+3vecOC=vec0`, then the ratio of `triangleABC` to area of `triangleAOC` is

Let O be an interior point of triangle ABC, such that 2vec(OA)+3vec(OB)+4vec(OC)=0 , then the ratio of the area of DeltaABC to the area of DeltaAOC is

Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + 3bar(OC) = 0 . Then the ratio of a DeltaABC to area of DeltaAOC is

Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + 3bar(OC) = 0 . Then the ratio of a DeltaABC to area of DeltaAOC is

if G is the centroid of triangleABC such that vec(GB) and vec(GC) are inclined at on obtuse angle, then

Let triangleABC be a given triangle. If |vec(BA)-tvec(BC)|ge|vec(AC)| for any t in R ,then triangleABC is

If O is the circumcentre and P the orthocentre of Delta ABC , prove that vec(OA)+ vec(OB) + vec(OC) =vec(OP) .

Let vec a , vec b and vec c be unit vectors such that vec a+ vec b- vec c=0. If the area of triangle formed by vectors vec a and vec b is A , then what is the value of 4A^2?

In a triangle OAC, if B is the mid point of side AC and vec O A= vec a ,\ vec O B= vec b ,\ then what is vec O C ?

Statement 1: let A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k) be two points. Then point P(2 vec i+3 vec j+ vec k) lies exterior to the sphere with A B as its diameter. , Statement 2: If Aa n dB are any two points and P is a point in space such that vec(PA).vec(PB) >0 , then point P lies exterior to the sphere with A B as its diameter.

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)